# atan#

ivy.atan(x, /, *, out=None)[source]#

Calculate an implementation-dependent approximation of the principal value of the inverse tangent, having domain `[-infinity, +infinity]` and codomain `[-π/2, +π/2]`, for each element `x_i` of the input array `x`. Each element-wise result is expressed in radians.

Special cases

For floating-point operands,

• If `x_i` is `NaN`, the result is `NaN`.

• If `x_i` is `+0`, the result is `+0`.

• If `x_i` is `-0`, the result is `-0`.

• If `x_i` is `+infinity`, the result is an implementation-dependent approximation to `+π/2`.

• If `x_i` is `-infinity`, the result is an implementation-dependent approximation to `-π/2`.

Parameters:
• x (`Union`[`Array`, `NativeArray`]) – input array. Should have a floating-point data type.

• out (`Optional`[`Array`]) – optional output array, for writing the result to. It must have a shape that the (default: `None`) inputs broadcast to.

Return type:

`Array`

Returns:

ret – an array containing the inverse tangent of each element in `x`. The returned array must have a floating-point data type determined by type-promotion.

This function conforms to the Array API Standard. This docstring is an extension of the docstring # noqa in the standard.

Both the description and the type hints above assumes an array input for simplicity, but this function is nestable, and therefore also accepts `ivy.Container` instances in place of any of the arguments

Examples

With `ivy.Array` input:

```>>> x = ivy.array([0., 1., 2.])
>>> y = ivy.atan(x)
>>> print(y)
ivy.array([0.   , 0.785, 1.11 ])
```
```>>> x = ivy.array([4., 0., -6.])
>>> y = ivy.zeros(3)
>>> ivy.atan(x, out=y)
>>> print(y)
ivy.array([ 1.33,  0.  , -1.41])
```

With `ivy.Container` input:

```>>> x = ivy.Container(a=ivy.array([0., -1, 1]), b=ivy.array([1., 0., -6]))
>>> y = ivy.atan(x)
>>> print(y)
{
a: ivy.array([0., -0.785, 0.785]),
b: ivy.array([0.785, 0., -1.41])
}
```
Array.atan(self, *, out=None)#

ivy.Array instance method variant of ivy.atan. This method simply wraps the function, and so the docstring for ivy.atan also applies to this method with minimal changes.

Parameters:
• self (`Array`) – input array. Should have a real-valued floating-point data type.

• out (`Optional`[`Array`]) – optional output array, for writing the result to. It must have a shape that (default: `None`) the inputs broadcast to.

Return type:

`Array`

Returns:

ret – an array containing the inverse tangent of each element in `self`. The returned array must have the same data type as `self`.

Examples

```>>> x = ivy.array([1.0, 0.5, -0.5])
>>> y = x.atan()
>>> print(y)
ivy.array([ 0.785,  0.464, -0.464])
```
Container.atan(self, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)#

ivy.Container instance method variant of ivy.atan. This method simply wraps the function, and so the docstring for ivy.atan also applies to this method with minimal changes.

Parameters:
• self (`Container`) – input container. Should have a real-valued floating-point data type.

• key_chains (`Optional`[`Union`[`List`[`str`], `Dict`[`str`, `str`]]]) – The key-chains to apply or not apply the method to. Default is `None`. (default: `None`)

• to_apply (`bool`) – If True, the method will be applied to key_chains, otherwise key_chains (default: `True`) will be skipped. Default is `True`.

• prune_unapplied (`bool`) – Whether to prune key_chains for which the function was not applied. (default: `False`) Default is `False`.

• map_sequences (`bool`) – Whether to also map method to sequences (lists, tuples). (default: `False`) Default is `False`.

• out (`Optional`[`Container`]) – optional output container, for writing the result to. It must have a shape (default: `None`) that the inputs broadcast to.

Return type:

`Container`

Returns:

ret – a container containing the inverse tangent of each element in `x`. The returned container must have a floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.Container(a=ivy.array([0., -1, 1]), b=ivy.array([1., 0., -6]))
>>> y = x.atan()
>>> print(y)
{
a: ivy.array([0., -0.785, 0.785]),
b: ivy.array([0.785, 0., -1.41])
}
```